A Stochastic Formulation of the Bass Model of New-Product Diffusion

In the past several decades, new-product diffusion models has been an active area of research in marketing (see, e.g., Mahajan, Muller, and Wind 2000, and Mahajan and Wind 1986). Such models are useful because they can provide important insights into the timing of initial purchase of new products by consumers. Much of the work in this area has been spawned by a seminal paper of Bass (1969), in which it was postulated that the trajectory of cumulative adoptions of a new product follows a deterministic function whose instantaneous growth rate depends on two parameters, one of which captures a consumer?s intrinsic tendency to purchase, independent of the number of previous adopters, and the other captures a positive force of influence on a consumer by previous adopters. While Bass?s model, or the Bass Model (BM), yields an S-shaped cumulative-adoptions curve that has proven to provide excellent empirical fit for a wide range of new-product-adoptions data sets (especially for consumer durables), there also has been a common belief (see, e.g., Eliashberg and Chatterjee 1986) that it would be of interest to have an appropriate stochastic version of his model. The purpose of this paper is to formulate and study a stochastic counterpart of the BM. Inspired by a very early paper of Taga and Isii (1959), we formulate the trajectory of cumulative number of adoptions as a pure birth process with a set of state-dependent birth rates that are judiciously chosen to closely parallel the roles played by the two parameters in the deterministic BM. We demonstrate that with our choice of birth rates, the resulting pure birth process exhibits characteristics that resemble those in the BM. In particular, we show that the fraction of individuals who have adopted the product by time t in our formulation agrees with (converges in probability to) the corresponding deterministic fraction in a BM with the same pair of parameters, when the total number of consumers in the target population approaches infinity. Our formulation, therefore, supports and expands the BM by having explicit micro-level stochastic interactions amongst individual adopters.Pure Birth Processes, Diffusion Models, New-Product Adoptions, Epidemics,

Congestible Public Goods and Indeterminacy in a Two-sector Endogenous Growth Model

This paper develops a new mechanism for local indeterminacy in a constant-return, two-sector, human capital enhanced growth model, with productive public spending financed by the income taxation in the goods sector. The use of productive public goods services is subject to an external congestion effect in association with the quantity of aggregate physical as well as human capital used in the economy. We establish local indeterminate equilibrium paths driven by the congestion effect. The possibility of local indeterminacy emerges because under constant returns, the congestion effect reduces the marginal contribution of public goods services and increases the marginal contribution of physical as well as human capital, thereby making the social marginal products to deviate from those of the firm’s perspective.two-sector model, indeterminacy, congestion

SCMA with Low Complexity Symmetric Codebook Design for Visible Light Communication

Sparse code multiple access (SCMA) is attracting significant research interests currently, which is considered as a promising multiple access technique for 5G systems. It serves as a good candidate for the future communication network with massive nodes due to its capability of handling user overloading. Introducing SCMA to visible light communication (VLC) can provide another opportunity on design of transmission protocols for the communication network with massive nodes due to the limited communication range of VLC, which reduces the interference intensity. However, when applying SCMA in VLC systems, we need to modify the SCMA codebook to accommodate the real and positive signal requirement for VLC.We apply multidimensional constellation design methods to SCMA codebook. To reduce the design complexity, we also propose a symmetric codebook design. For all the proposed design approaches, the minimum Euclidean distance aims to be maximized. Our symmetric codebook design can reduce design and detection complexity simultaneously. Simulation results show that our design implies fast convergence with respect to the number of iterations, and outperforms the design that simply modifies the existing approaches to VLC signal requirements

Import Tariffs and Growth in a Model with Habits

This paper studies the relationship between tariffs and economic growth in a two-country AK growth model. We find that a sufficiently higher tariff can increase or decrease economic growth, which depends on the levels of productivity coefficients in both countries. Moreover, the Ricardian theorem of comparative advantage holds in the long-run equilibrium and local indeterminacy emerges in the case of incomplete specialization under milder conditions compared with conventional literature.AK growth model, two-country, tariffs, growth, indeterminacy